Equations of Love
by Time Signature
Summary: N found mathematical equations beautiful, because the answers were simple – just right or wrong, black or white. Then he meets Touko, and even though she is more complex than Fermat's Last Theorem, he finds her more beautiful. A collection of unrelated Ferriswheelshipping drabbles or one-shots, centered on mathematical terms.
1. one, a proof too perfect

Equations of Love

Time Signature

Summary: N found mathematical equations beautiful, because the answers were simple – just right or wrong, black or white. Then he meets Touko, and even though she is more complex than Fermat's Last Theorem, he finds her more beautiful. A collection of unrelated Ferriswheelshipping drabbles or one-shots, centered on mathematical terms.

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><p>Now, fear the darkness within you that you cannot escape. "Sette," Shikata Akiko<p>

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><p>one, a proof too perfect<p>

Touko hugged her knees on the small bed in a rather rural Pokémon Center in Johto. It was now well into her third year of her journey, renewed to search for the other missing hero shortly after she had become Champion. She had quickly told Cheren that she had no intention of sitting around in the League waiting for challengers and signing paperwork when there were still leftover Plasma members to take care of.

True, she had been asked by the International Police to find the seven sages. However, but more than that, she wanted to see N again. She wanted to ask him why he had simply left with a "farewell." She wanted to tell him that they could see the world together.

Before she had faced N in the final battle, she had met the two women responsible for his upbringing. "There is nothing more beautiful and terrifying than innocence," Concordia had told her then. Touko had never seen it that way – innocence was the symbol of childhood, of unforgotten dreams and ambitions. But after she had heard the goddess say so, she could not help but agree.

N was the embodiment of innocence, and he was the proof too perfect that showed the truth of her statement.

Somewhere in her heart she was a tiny bit scared of N. She was scared of how pure he was, how blindly trusting he could be, how much empathy he could put into a statement that he had never seen the other side of. She was scared of how he could trust Ghetsis, even after his motives had been shown. But precisely because of that, she wanted to be with him.

She wanted to be the answer to his equation that would change the world.

Sighing, Touko shook her head. It was too pointless of her, the savior of Unova, to have such feelings for an international criminal. She apathetically clicked the power button on the remote control to the only remotely modern technology in the room. The announcer on the television was showing a frighteningly familiar sign.

The P for Plasma.

Driven with hate and fear, her hand instinctively reached for her waist, and then she realized that she had taken off her Pokeball belt. She could, over the crackling speech of the announcer, hear her partners angrily rocking their cages (she could not deny that at least a part of N's speech had reverberated with her).

Grabbing the belt, she numbly stared at the screen. Had they succeeded in a coup while she had not been in Unova? Was it her fault for prioritizing N over any of the other sages?

The display switched to a photo of a beautiful girl around her age, much more beautiful than she could ever dream of being. The voice continued, "And the second heroine Mei has defeated the reformed Team Plasma of Unova. It seems as though the heroine of two years ago has deserted her mission to capture the sages, as all were present when we arrived to the scene." The screen abruptly flickered out, then back in. "However, Unova has been saved by a very talented young girl – Mei, a superb trainer and currently the most popular actress in the movie world. With her we need not fear that she will follow in the footsteps of her predecessor."

It switched once again, this time to a scene of wreckage, such as after a powerful battle. The edge of the screen stated that this was now live feed. Once again, in the center stood the girl, who looked impeccable though she had most likely been just fighting. And in the corner, a flash of tea green – could that be N?!

The display flickered. She stared, willing it to stay on. It flickered multiple times rapidly, and then turned off.

The girl grabbed the roots of her hair with one hand, while throwing the remote onto the bed with so much force a few feathers fluttered from the covers. Her Pokémon looked up worriedly from inside the red-white spheres.

She grit her teeth and roughly stood up. Clipping the belt to her waist, she stuffed everything into her bag and prepared to leave. She thanked the Nurse Joy, who looked up from whatever she had been doing and waved goodbye, and stepped out the door. Once she had found a suitable clearing for taking off, she summoned her legendary dragon, the one connection that she could guarantee with N.

"Take me to Unova," she whispered. He nodded, then powered up his tail engine to take off.

As she flew over an endless ocean, her unkempt hair (so different from the girl on the screen) whipping her face, she suddenly realized that she was asking a ridiculous amount from him. Unova and Johto were literally half the world apart. She was asking him to do that in one flight.

N's voice came back to her – "I will separate Pokémon and people, and only then will Pokémon become perfect beings!"

Was she doing the right thing?

She was scared of herself. She was scared of how much negative things she carried inside her.

She was scared of tainting N. She was terrified of how pure he was, but more so of herself.

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><p>AN: Thank you for reading! This was the first one, and I have another in mind, so that should come shortly. Maybe weekly updates, I don't know. I personally love math, so that's why this was born.

Please tell me what you think! Good, bad, I should toss it in the trash and rewrite the whole thing…

Requests are also welcome! I can't guarantee that I'll write it, but suggestions such as "such-and-such" math term, N POV, or "more fluff!" will be taken into consideration.

See you soon,

Time Signature


	2. two, absolute convergence

Equations of Love

Time Signature

Summary: N found mathematical equations beautiful, because the answers were simple – just right or wrong, black or white. Then he meets Touko, and even though she is more complex than Fermat's Last Theorem, he finds her more beautiful. A collection of unrelated Ferriswheelshipping drabbles or one-shots, centered on mathematical terms.

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><p>And the worlds entwining together are crumbling down. "Katayoku no Tori," Shikata Akiko<p>

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><p>two, absolute convergence<p>

Any series that is absolutely convergent within itself is convergent itself. That was a simple fact that N had known for a long time. Even if the values interchanged signs (pluses and minuses), the series would eventually come together. The sum was definite. The same, no matter whether it was pluses or minuses.

Of course, the sums of the original series and the new one were different. Again, that was a fundamental principle of math. But they both converged.

What about Touko and himself? Would their paths converge? Would they meet again?

He had no specific place in mind to go. After he had lost to Touko in the final battle, he had lost all direction for himself – what of his world where Pokémon were truly happy?

What of his father, that man, who had lied for all these years?

Did the laws of mathematics allow a series without a specific summation notation to still converge?

Gazing at the azure sky above him, he traced it to where it met the ground at the horizon. The sky and the ground, which were so far apart, converged together. He looked at the majestic dragon beside him. He, too, was once one with the other, which was so opposite in color and symbolism and so much more.

So if opposites converged, would he and Touko?

Were they opposite enough for their paths to cross again? Were they complex enough of equations so even if the starting points of the equations were different, their lines would eventually become one?

He wanted to see the bright brown of her hair, which contrasted nicely with his (like a grand tree in Pinwheel forest). He wanted to see the crystal blue of her eyes, which were the opposite in shade.

If he had been a king, Touko would be a queen forever. Because they were opposites.

He could not solve the equation that would change the world. But he had found the solution to the equation that would solve his world, and that was Touko.

That was Touko, from her baseball cap to her immeasurable bonds with her Pokémon to her favorite shorts which were reminiscent of Reshiram.

But if his equation only had one solution, his graph would be only a point. Then his path could never converge with Touko's.

But wait, yes it could. If his solution was Touko, then his equation did not converge with Touko's, but his equation was Touko's. It was not a matter of convergence. It was a matter of identity.

He closed his eyes. He had proved that he could converge with Touko. However, the last time he had relied on calculations to execute the precisely identical results he had failed. He had not factored in Touko.

Even if he had proved that they would converge, there was nothing to assure him that that would happen in reality. His proof was the ideal. The truth he did not know.

He turned to look at the legendary. If the dragon would converge with his counterpart, and Touko still was with her, then Touko and he would meet when the dragons converged.

He had proved, once again, that they would meet. No matter what.

And yet, after that great battle in the castle, he found himself doubting his precise proofs and infallible axioms.

He found himself whispering, "But will I see her again?"

* * *

><p>AN: Thank you for reading! Please tell me what you think!

Pff, this time I used way too much math. Did I fry anyone's brains? I'm pretty sure I fried my own. I'm sorry if I did, but this is what I imagine N's head to be like…

Requests are also welcome! I can't guarantee that I'll write it, but suggestions such as "such-and-such" math term, so-and-so POV, or "more fluff!" will be taken into consideration.

Next: Solving for X, requested by Ten-Faced.

For PokeWrite's The Great Race Competition, 11.

See you soon,

Time Signature


	3. three, solving for x

Equations of Love

Time Signature

Summary: N found mathematical equations beautiful, because the answers were simple – just right or wrong, black or white. Then he meets Touko, and even though she is more complex than Fermat's Last Theorem, he finds her more beautiful. A collection of unrelated Ferriswheelshipping drabbles or one-shots, centered on mathematical terms.

three, solving for x

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><p>Even if you outstretch your hand, there is nothing you can touch. "Hontou no Oto," KOKIA<p>

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><p>Just like there was a quadratic formula that solved any second-degree equation, there were formulas that solved for third-degree equations, and fourth-degree, and everything else.<p>

Most of them just hadn't been proved yet – those calculations were too strenuous for present computers.

How long would it take for the formula for an infinite-degree equation to be found? Even in N's mind, which was undoubtedly one of the smartest in the past few centuries, the idea was fuzzy. He had no idea what it would look like. Perhaps it would be an unbelievably ugly thing, with so many roots and fractions to take care of.

Perhaps it would be the most elegant thing in the history of mathematics.

How long would it take for the formula of him and Touko to be found? And when it was found, would it be ugly or beautiful?

N was never one to blindly believe. He based all of his statements on firm facts and proofs, and only then would he think anything.

But somehow he had an intuitive feeling that their formula would be elegance in its utmost simplicity.

It would be elegance like the Ferris Wheel they had ridden together (the only time they had spent in just peace). The circular motions and mechanics fit perfectly together just like he and Touko did.

She was the first girl he had ever truly known. Anthea and Concordia were his sisters and caretakers; they were girls, but more than that they were family.

Touko was the first girl he had ever come into close contact to.

Touko was the only girl he would ever share his status with. His status as hero (no, not really, he wasn't a hero anymore) or as a sovereign.

But he knew, based off her personality, the relationship they had, the things she had said, that she would never share his status as sovereign. She would refuse to rule over Team Plasma with him.

He didn't regret being the King of Team Plasma. He didn't regret believing the lies that Ghetsis had told him about saving Pokémon, because it had given him direction. And still, sometimes he wondered if things had been different, Touko would accept him.

If he had not been the King of Team Plasma, would Touko agree to be with him? If he had opposed Ghetsis much earlier, would things have changed?

He shook his head. No, that was not possible. It was precisely because he had been the King of Team Plasma that he had met Touko. That was how solving equations worked.

Linear systems had one solution. Quadratic equations had two, but it was an extraordinarily low probability that he would have been able to change into the other solution. And as the variables increased, it only grew less probable that he would meet Touko otherwise.

He didn't regret leading Team Plasma. He just sometimes imagined the fuzzy future that would have happened, had he taken the other path.

That was why he liked math – there were only clear-cut answers, and no matter which path one took it would always lead to the same answer.

Not like he and Touko.

* * *

><p>AN: Thank you for reading! Please tell me what you think! Good, bad, I should toss it in the trash and rewrite the whole thing…

Requests are also welcome! I can't guarantee that I'll write it, but suggestions such as "such-and-such" math term, so-and-so POV, or "more fluff!" will be taken into consideration.

Haha, these are getting shorter and shorter aren't they?

For The Great Race Competition 7, "fuzzy."

See you soon,

Time Signature


	4. four, asymptote

Equations of Love

Time Signature

Summary: N found mathematical equations beautiful, because the answers were simple – just right or wrong, black or white. Then he meets Touko, and even though she is more complex than Fermat's Last Theorem, he finds her more beautiful. A collection of unrelated Ferriswheelshipping drabbles or one-shots, centered on mathematical terms.

* * *

><p>Right now, what are you doing, what were you doing? I'm right here. "VOiCE," LovelyP<p>

* * *

><p>four, asymptote<p>

N felt his heart accelerate whenever his eyes caught a flash of wavy brown. And then his heart accelerated down when he realized it was not _her._

His breath caught whenever he saw a pink bag in the crowd, and was let out just as quickly when he saw the person carrying it.

He didn't know what these symptoms were. They had started shortly after he had ridden the Ferris wheel with her. He didn't want to find out. These were foreign thoughts, better off being forgotten. He had a quest to fulfill. He needed to liberate all of those poor Pokémon.

Those thoughts were better not touched. He needed to drag his mind away from them (and that was so difficult, seeing as he could only focus on one thing at a time) and think about his dream. His ultimate ideal of what the world should truly be like.

The more he tried to push these feelings out of his mind, the more he pondered them. He could still recall the girl's arm that he had grabbed to prevent her from going after Team Plasma. It had been a healthy, slightly tanned shade and much thinner than he had imagined. He thought he could break her wrist if he even put a tiny amount of force in his hand.

Before he started his journey, his final step to his dream of Pokémon freedom, he had never imagined that he would be scared of hurting someone. Everyone that he knew gradually opened up to him, and he had never hurt any of his friends.

He was afraid of touching her, in fear that she would break apart like the antique vases and chandeliers inside his castle (he had seen how beautifully those broke from the times his friends had still been hostile).

A few weeks later, he sees her again. He tells her, "It is not possible for us to touch! We are separated as how the two halves of hyperbolas are on opposite sides of the two asymptotes."

She raises an eyebrow in disbelief. Her partner next to her mimics her, and even though he cannot imagine what she is no doubt saying inside herself he can hear the Pokémon thinking, "What are you talking about? She doesn't get it."

She comes up in his face. He jerks backward quickly, slightly surprised at the size of her storm-blue eyes. She flicks his forehead, failing to stifle a giggle.

He can't tell what has happened. No one has ever flicked his forehead before – he is the King of Team Plasma. He sees her crystalline-blue eyes sparkling with mirth and suddenly, illogically, has the urge to flick _her_ forehead.

"See! I can totally touch you! You're not air or a ghost-type, so I can touch you! I had no idea what you were saying N, but then again, that's pretty much all the time…"

She starts rambling, so he flicks her forehead back.

"Yes, that seems so."

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><p>AN: Thank you for reading! Please tell me what you think! Good, bad, I should toss it in the trash and rewrite the whole thing…

Requests are also welcome! I can't guarantee that I'll write it, but suggestions such as "such-and-such" math term, so-and-so POV, or "more fluff!" will be taken into consideration.

This is dedicated to Ten-Faced, who thinks I can only write angst with the prompt "asymptote." Hah.

For The Great Race Competition 10 – "Drag your thoughts away from your troubles—by the ears, by the heels, or any other way, so you can manage it." – Mark Twain

See you soon,

Time Signature


	5. five, non-euclidean geometry

Equations of Love

Time Signature

Summary: N found mathematical equations beautiful, because the answers were simple – just right or wrong, black or white. Then he meets Touko, and even though she is more complex than Fermat's Last Theorem, he finds her more beautiful. A collection of unrelated Ferriswheelshipping drabbles or one-shots, centered on mathematical terms.

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><p>five, non-euclidean geometry<p>

Come with me on this never ending journey…forget everything and sleep on my sleeves. "Tsunagi Chou," arcane753

Time either goes too fast or too slow. True, it was true that humans could control time to a certain extent – for example, if one rode a Garchomp running at full speed. If one could go faster than speed itself, time would slow down. This was the theory of relativity, well known by any scientist worth their weight. (Although at the time of its conception it had been thought impossible, it had been changed after the invention of Pokeballs).

So of course, N knew it. He could not help but think that it fit his situation perfectly. The theory of relativity could be modeled by non-Euclidean geometry (specifically, the hyperboloid type) and it was a fact that in that world, the sum of a triangle's interior angles was zero. Therefore one could infer that the lengths of the triangle's sides were infinite. No matter how much he went, how fast he went, he could not reach Touko.

Why?

He didn't have an X-transceiver. He had never thought he would need one – why would he? But he was deeply regretting the fact that he had turned down Touko's offer to look at X-transceivers together. She had gone off to some region on the other side of the world and he had no idea where she was. He was deeply worried.

What if she had found another region in trouble and had decided to become the heroine there? What if she had decided that she would live there?

What if she had found someone to live with?

He clenched his fist like any shape would in a hyperbolic plane. For some reason he could not fathom (even with his mind which was more powerful than probably any human's) he felt strangely angry about that concept. No matter how much he thought of the reasons why he would feel so, he could not find a way to rationalize his irritation.

He somehow knew, however, that this irrational fear and anger would not subside until she returned and he could see her once again.

Then he realized that he had no idea when she would come back, and then he clenched his fist again (there were red crescents where his nails had cut into his palm last time).

He looked around at the crowded amusement park in Nimbasa that he had come to (to remember how they had ridden the Ferris wheel together). All around were happy families and couples.

"Boo!" exclaimed a very familiar voice from behind him. He could not believe it, but when he turned around, it was her.

And he felt all that anger and fear and worry subsiding, being replaced by a quickly expanding joy from seeing her.

All shapes drawn on ellipsoid planes seem larger compared to the same shape on a Euclidean plane.

Every time he saw Touko, she seemed to be more and more glorified (or was that just him)? She seemed to be much too good for someone like him.

"You are to me as triangles are to a hyperboloid plane," he told her.

She just placed one hand to her head and cracked a grin.

And suddenly, everything was all right.

* * *

><p>AN: Thank you for reading!

Please tell me what you think! Good, bad, I should toss it in the trash and rewrite the whole thing…

Requests are also welcome! I can't guarantee that I'll write it, but suggestions such as "such-and-such" math term, N POV, or "more fluff!" will be taken into consideration.

I just saw a presentation on non-Euclidean geometry at my math club, so…this happened.

Next is "subtraction."

For The Great Race 9, "Time either goes too fast or too slow."

See you soon,

Time Signature


	6. six, subtraction

Equations of Love

Time Signature

Summary: N found mathematical equations beautiful, because the answers were simple – just right or wrong, black or white. Then he meets Touko, and even though she is more complex than Fermat's Last Theorem, he finds her more beautiful. A collection of unrelated Ferriswheelshipping drabbles or one-shots, centered on mathematical terms.

six, subtraction

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><p>There must be a reason that we met…I think my heart will stop beating. "Shinpakusu #0822," papiyonP<p>

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><p>Touko privately thought that N was part machine. He certainly had the brains to be a supercomputer. And she did not mean to be insulting of the effort he was making to express himself, but he still was missing a few crucial emotions that humans had. He was like a machine, so whenever one part broke or disappeared he broke as well.<p>

She hid a tiny smile. She had become much more indulgent of N over the years. It had been about five years since she had first met him, and she now was an adult with a respectable job. N in turn simply continued his journey around the world (she had no idea how he was making money, as he hated to battle trainers for any reason) and sometimes popped in.

The odd thing about his journey was that although he wandered off on his own, he needed to call her at least one time every three days to feel "safe," he said. There had been that one time that she had been unable to pick up on his call because she was battling the Elite Four (electronics were forbidden), and after that there had been a flood of messages and calls to her X-transceiver. She refrained from mentioning to him that it was borderline stalker action. He probably had had no one to tell him about it (and he used to have official stalkers called the Shadow Triad) so she needed to tell him about it little by little.

Going by her machine analogy, that meant that N considered Touko a part of him. She was touched by that. He had told her often that he considered her his first human friend (and right now, that was enough).

He was probably still not ready enough for romance. She would indulge him in this lukewarm relationship until he was ready or until he no longer needed her.

She would indulge him in whatever he wanted. It was her present of sorts – she would let him become human, little by little, in his own way. If he found some other lovely girl to be with, so be it.

Her emotions were of no matter in this situation. It was her responsibility to make sure he would fit into society, as she was the one who had brought him out to it from his impenetrable castle. If she thought about it this way he was like Rapunzel as well.

He was like a machine, and he was also like a princess. Well, he certainly did have the hair.

She failed to stifle her giggle this time.

On the other side of the screen, the man in question asked what she was finding so funny. She quickly replied "no, nothing," and then asked him what it was like in Kalos.

He burst into rapid talk (she had come a long way now – she could pick up on about eighty percent of what he was saying) about how there were statues of Zekrom and Reshiram over there, if she had heard correctly.

At the end, he told her, "I wish you were here to look at them too."

She smiled sadly. "Yeah, me too."

She's the one that's breaking when he's not there, not him.

* * *

><p>AN: Thank you for reading!

Please tell me what you think! Good, bad, I should toss it in the trash and rewrite the whole thing…

Requests are also welcome! I can't guarantee that I'll write it, but suggestions such as "such-and-such" math term or "more fluff!" will be taken into consideration.

For the Great Race competition, 13 (some assembly required). I took some more liberties with this one.

See you soon,

Time Signature


End file.
